Summary: JOURNAL OF COMPUTATIONAL PHYSICS 146, 546­569 (1998)
ARTICLE NO. CP986027
A Taylor­Galerkin Method for Simulating
Nonlinear Dispersive Water Waves
D. Ambrosi and L. Quartapelle
Dipartimento di Matematica, Politecnico di Torino, corso Duca degli Abruzzi 24,
10129 Turin, Italy; and Dipartimento di Fisica, Politecnico di Milano,
piazza Leonardo da Vinci, 32, 20133 Milan, Italy
Received November 19, 1996; revised May 12, 1998
A new numerical scheme for computing the evolution of water waves with a mod-
erate curvature of the free surface, modeled by the dispersive shallow water equations,
is described. The discretization of this system of equations is faced with two kinds
of numerical difficulties: the nonsymmetric character of the (nonlinear) advection­
propagation operator and the presence of third order mixed derivatives accounting for
the dispersion phenomenon. In this paper it is shown that the Taylor­Galerkin finite
element method can be used to discretize the problem, ensuring second order accu-
racy both in time and space and guaranteeing at the same time unconditional stability.
The properties of the scheme are investigated by performing a numerical stability
analysis of a linearized model of the scalar 1D regularized long wave equation. The
proposed scheme extends straightforwardly to the fully nonlinear 2D system, which

Source: Ambrosi, Davide - Dipartimento di Matematica, Politecnico di Torino

Collections: Mathematics